{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# create_counterfactual: Interpreting models via counterfactuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An implementation of the counterfactual method by Wachter et al. 2017 for model interpretability.\n",
    "\n",
    "> `from mlxtend.evaluate import create_counterfactual`    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Counterfactuals are instances that explain scenarios related to implication: \"if not x, then not y\" in a hypothetical context. For example, \"if I hadn't studied hard, my grade would be worse.\" \n",
    "\n",
    "In the context of machine learning, we can think of counterfactual instances from the training set for which we artificially change its features to change the model prediction. Changing features of a training example can be useful to interpret the behavior of the model.\n",
    "\n",
    "Note that this implementation for creating counterfactuals is model agnostic and works with any scikit-learn estimators that support the `predict` (and ideally `predict_proba`) method.\n",
    "\n",
    "\n",
    "In particular, the `create_counterfactual` implements the method described by Wachter et al. 2017 [1]. A good, short description of this method is also available in C. Molnar's Interpretable Machine Learning Book [2].\n",
    "\n",
    "\n",
    "\n",
    "In short, Wachter et al.'s method minimizes the loss\n",
    "\n",
    "$$L\\left(x, x^{\\prime}, y^{\\prime}, \\lambda\\right)=\\lambda \\cdot\\left(\\hat{f}\\left(x^{\\prime}\\right)-y^{\\prime}\\right)^{2}+d\\left(x, x^{\\prime}\\right).$$\n",
    "\n",
    "The left term, $\\lambda \\cdot\\left(\\hat{f}\\left(x^{\\prime}\\right)-y^{\\prime}\\right)^{2}$, minimizes the squared difference between the model prediction for the counterfactual $x'$, i.e., $\\hat{f}\\left(x^{\\prime}\\right)$, and the desired prediction (specified by the user), $y^{\\prime}$. Note that $\\lambda$ is a hyperparameter for weighting the importance of this left term over the second term, $d\\left(x, x^{\\prime}\\right)$.\n",
    "\n",
    "The second term, $d\\left(x, x^{\\prime}\\right)$, calculates the distance between a given instance $x$ and a generated counterfactual $x'$. In short, the second term will keep the generated counterfactual similar to the instance. In contrast, the first term maximizes the difference between the model prediction for the counterfactual and the desired prediction (for example, a different class label)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distance function is implemented as the absolute difference in each feature dimension scaled by the median absolute deviation (MAD):\n",
    "\n",
    "$$d\\left(x, x^{\\prime}\\right)=\\sum_{j=1}^{p} \\frac{\\left|x_{j}-x_{j}^{\\prime}\\right|}{M A D_{j}}.$$\n",
    "\n",
    "The MAD measures the spread of a given feature, using the median as its center:\n",
    "\n",
    "$$MAD_{j}=\\operatorname{median}_{i \\in\\{1, \\ldots, n\\}}\\left(\\left|x_{i, j}-\\operatorname{median}_{l \\in\\{1, \\ldots, n\\}}\\left(x_{l, j}\\right)\\right|\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general procedure for using the `create_counterfactual` function is as follows.\n",
    "\n",
    "1. Select an instance that you want to explain and specify the desired prediction $y'$ for this instance (this is usually different from its original prediction).\n",
    "2. Choose a value for the hyperparameter $\\lambda$\n",
    "3. Optimize the loss $L$ using the `create_counterfactual` function\n",
    "4. Optionally, as the authors recommend, you can repeat steps 2 and 3 by increasing $\\lambda$ until a user-defined threshold $\\epsilon$ is reached, i.e.,\n",
    "    - while $\\left|\\hat{f}\\left(x^{\\prime}\\right)-y^{\\prime}\\right|>\\epsilon$:\n",
    "        - increase $\\lambda$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "- [1] Wachter, S., Mittelstadt, B., & Russell, C. (2017). Counterfactual explanations without opening the black box: Automated decisions and the GDPR. Harv. JL & Tech., 31, 841., [https://arxiv.org/abs/1711.00399](https://arxiv.org/abs/1711.00399)\n",
    "- [2] Christoph Molnar (2018). Interpretable Machine Learning, [Chapter 6.1](https://christophm.github.io/interpretable-ml-book/counterfactual.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1 -- Simple Iris Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity, this example illustrates how to use the `create_counterfactual` function to explain a data instance from the iris dataset.\n",
    "\n",
    "Suppose we trained a logistic regression model on the iris dataset and pick the 16th training point for which we want to explain the prediction via counterfactuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True label: 0\n",
      "Predicted label: 0\n",
      "Predicted probas: [[9.86677291e-01 1.33226960e-02 1.28980184e-08]]\n",
      "Predicted probability for label 0: 0.9866772910539873\n"
     ]
    }
   ],
   "source": [
    "from mlxtend.data import iris_data\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "\n",
    "X, y = iris_data()\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X, y)\n",
    "\n",
    "x_ref = X[15]\n",
    "\n",
    "print('True label:', y[15])\n",
    "print('Predicted label:', clf.predict(x_ref.reshape(1, -1))[0])\n",
    "print('Predicted probas:', clf.predict_proba(x_ref.reshape(1, -1)))\n",
    "print('Predicted probability for label 0:', clf.predict_proba(x_ref.reshape(1, -1))[0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see above, that there is a predicted score of 98.6% probability for a class 0 membership. Now, we are going to push the prediction towards class 2 by setting `y_desired=2`. Moreover, we set the probability for class 2 to 100% via`y_desired_proba=1.`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Features of the 16th training example: [5.7 4.4 1.5 0.4]\n",
      "Features of the countefactual: [5.72271344 3.99169005 6.45305374 0.40000002]\n",
      "Predictions for counterfactual:\n",
      "\n",
      "Predicted label: 2\n",
      "Predicted probas: [[1.41639932e-04 3.13292297e-01 6.86566063e-01]]\n"
     ]
    }
   ],
   "source": [
    "from mlxtend.evaluate import create_counterfactual\n",
    "\n",
    "\n",
    "res = create_counterfactual(x_reference=x_ref, \n",
    "                            y_desired=2, \n",
    "                            model=clf, \n",
    "                            X_dataset=X,\n",
    "                            y_desired_proba=1.,\n",
    "                            lammbda=1, #  hyperparameter\n",
    "                            random_seed=123)\n",
    "\n",
    "print('Features of the 16th training example:', x_ref)\n",
    "print('Features of the countefactual:', res)\n",
    "\n",
    "print('Predictions for counterfactual:\\n')\n",
    "print('Predicted label:', clf.predict(res.reshape(1, -1))[0])\n",
    "print('Predicted probas:', clf.predict_proba(res.reshape(1, -1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see above, the counterfactual is relatively similar to the original training example, i.e, only the 3rd feature has changed substantially (from 1.5 to 6.45). The predicted label has changed from class 0 t class 2. \n",
    "\n",
    "Interpretation-wise, this means increasing the petal length of a Iris-setosa flower may make it more similar to a Iris-virginica flower."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2 -- Simple Iris Example with Decision Regions and Threshold Stopping Criterion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is similar to Example 1; however, it is based on a 2D iris dataset containing only petal length and petal width features so that the results can be plotted via a decision region plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from mlxtend.plotting import plot_decision_regions\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "X, y = iris_data()\n",
    "X = X[:, 2:]\n",
    "clf = LogisticRegression()\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting decision regions\n",
    "ax = plot_decision_regions(X, y, clf=clf, legend=2)\n",
    "\n",
    "\n",
    "scatter_highlight_defaults = {'c': 'red',\n",
    "                              'edgecolor': 'yellow',\n",
    "                              'alpha': 1.0,\n",
    "                              'linewidths': 2,\n",
    "                              'marker': 'o',\n",
    "                              's': 80}\n",
    "\n",
    "ax.scatter(*X[15],\n",
    "           **scatter_highlight_defaults)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The big, highlighted point in the plot above shows the 16th training datapoint. \n",
    "\n",
    "The following code will create a counterfactual with the same settings as in Example 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "counterfact = create_counterfactual(x_reference=X[15], \n",
    "                                    y_desired=2, \n",
    "                                    model=clf, \n",
    "                                    X_dataset=X,\n",
    "                                    y_desired_proba=1.0,\n",
    "                                    lammbda=1, \n",
    "                                    random_seed=123)\n",
    "\n",
    "\n",
    "ax = plot_decision_regions(X, y, clf=clf, legend=2)\n",
    "ax.scatter(*counterfact,\n",
    "           **scatter_highlight_defaults)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see above, the counterfactual primarily moved along the x-axis (petal length) so that the prediction between the rerence point and the counterfactual changes from class 0 to class 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots are based on repeating this procedure with different lambda values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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c+vgEkxa/XeJ+OvXsqAm9gpX7NtQYs8YYI8aYjsaYTu6vRcaYye5kjzFmgjGmnTHmcmPMlcaYH8ofuvInLbv0ZPyi6rfgWP06NZgwpg9Lxs/hXOo5q8PxqiwFVW/Sz7oKrIX6bBVB+tn0MvepKoaOOyifCAmLIDiqvtVhWCImKpJJd19P3BtfkZbi38tLlKWg6k1IuKvAWqjPvWmEhIeUuU9VMfRhYqV8oHaNcKbc25eH3v6a6x4bTmStCO8nWWDgLf2Z/sYMcoOzyUjLIjjCSdapXOrUq83TI5/zOMPV24zXfsOvJ25mHIwifwx//+cJhDki8vv0NEvW22zcsszWrQj+EocvaMJXykdqRYYx5b5+jHtnLr0fHkrNOjWsDskje4iNun3qEBxj5+SGVJJSU4i5oQb1LmvO8R1JxH0aR9PeDen2QMlmvI54cBgAyz5eTvrZwziDndjtDto+0pSazSI8nuOteFwRxeWy8Jc4fEWHdJTyoRrhoUy9fwCr3p3H6ZOnrQ7nAku+XEqbUU1pdU0zGrdpTEZCFi1G/z6jVWrm0nxULCd3JGOz2zzOeG02PJYlXy4t1O+IB4cxafHbfLhqKi3aNqfTI5cQ1bJGsecULB57auPt88r87+UPcfiKJnylfCwiLJhpYwfyw+SFnDruXyuIepvRmp2VRc1WEZw7ke7xcyj9rFlP53hrUxHF5bLwlzh8RRO+UhUgLCSIKWMHsHbaQk4mlGnKSYXwNqPV4XSSsjeNsJgQj59D6WfNejrHW5uKKC6Xhb/E4Sua8JWqIKHBQUx7cBA/fxhHYvwJq8MBvM9oNSk2DsxMIPqyqFLNeC04ezctJY2d0w8Ummm7e+YhziSl5s/ubdOudaE4ivZbNM6KnGl7sZnHlRlHZRB/XvNl2qr9/hucusD3M15h+r2BV8iqaJlZ2Tz8XhwdRl9Hvab1rA7H67rzpX1Kp2BhM69Iu3vmIYIJJSMjg9DwENLS0mh7d/P8zw/OTaBb925e+63op2M8xX5wbkKhWb2B9pTOqHZ3FbsEgSZ85TOrZ7zKxFtbE6nPX18gOzuHcVOX0PWBG6gVXdP7CQHk1cdfI6pfaP7sXYDkfWdIXnae597+s9fPreTPsZXVxRK+Dukon+k0dCzPffyj1WH4JYfDzj292rFtVfkXKvM3gVKA9cSfY6sImvCVz0TWqo0Eh1sdht+6pn0zLsvMYuOS9VaH4lOBUoD1xJ9jqwg68UqpSvTwoK5MXbqRdQvW0n3IlVaHUyKexrCB/GPBwcEcnXGU+v2jCI6xk3Eih2NLk4kIiuTpkc8RGh7CsenHPI7hv/r4a5U6Nu6pfrF+7noYzgVj+FWRJnylKtnY/l34cPlmfvrmB3oMu9rqcC7K00zTjyd9Qk56Lm3vbp6//+zxxWc5sjyH7HPZOMIcpCenU39QHTr2b+Eu4p7j0MxEMjJcSx93696N9evWV+oMVk9/lvVz17uKx8v25C/LXJWXYdaEr5QF7rm+E5+s2MIPs1dz9chrrQ6nWJ6WU67TJ5Jj3yUV2n+29b2NCKsdSv0m9Tj223HOnTpP4vJkWg1qQlTLGrQZ1dRdCH0JcBVLfb1Mc1n+LAyH3cv2BGyBtrR0DF8pi4zp05GrQxys/mKF1aEUy1NRMzjGTkba7zNvvc3WhdLPtK0I1a1A64kvdrxqDMwA6gO5wFRjzFtF2gjwFnADcA642xizsbzXVirQjbq2HcE/7GTpp9/S+/bryt2ft2fsi46/e3vOPq+oWfCxxYwTOQRH/D7zNm82blht1wYwRWfrQvEzbQv264ti6cWemS/umsHBwZVeS7CKL+7ws4GnjTFtgSuBR0TksiJtBgGt3V9jgUk+uK5SVcJNV7dlcN0afDdjWbn6yRujjuoXSrcX2xJ6jY24hXHkNs2g24ttieoXyseTPmH6GzPy2+Q2zSBuYRyh19jy23zx4Zf5s009zTRNWpGKLcNR4tm6nmanVsQM1qJ//pL8WXZOP0AG54s9p6op9x2+MSYBSHC/ThWRnUBDYEeBZsOAGe5tDdeKSC0RiXWfq6qQjEzde7IshnRvg2PjPmZ/sITr7xlQpv2ai45R5618WXAs3dP4e9HVMAuOpXvaa/aOh8ZccKzo/rMDBg9g9/Y9rH/J8360nvotb7HU2/aNnq4ZERFB45ExlVpLsJJPi7Yi0gzoDPxU5KOGwOEC7+Pdxy5I+CIyFtdvAYx5+mV6DR3tyxBVBYvpOpjJi75j3A2drQ4l4Azs0pIgu/DJtMX0e2BQqZP+iaMnadasbf77vLH0gzOP5x/zPP7ekPPHC4+37z76+z/X4vaaLW9C9PUetkX//OD9z/L0yOc8jusXPKcq8VnRVkQigDnAk8aYM0U/9nCKx2UTjDFTjTFdjTFdNdkHnuaXX8P+46lWhxGwrru8Bfe0a0Tc5AWUdtmTopOIPI2lFzf+XprVMP1VWSZR6cSrMhARJ65k/6kx5isPTeKBxgXeNwKO+uLaSlU117ZvhsNuZ/LEeQx8ZGiJ7/QH3tLf9Sz7cNddqkmxseeDeIIinSx/bi3BEU5yUg2Z57L47m8/kXU2GwykfnqW9ne2Jjcnt9DCZxfbnrAylHbRsqJ//pJMoirLOYHMF0/pCPA+sNMYM76YZvOAR0VkJtADSNHxe6WKd1XbxjjsNt5+Zy6DHh2Gzeb9l/GiY9TBwcGER4UXmgF7ZNEJcsihcd9oQuoFkX48k4OzjvPbrER+I5HQ8BBy0nNpenfdYrcnrAxl2VqwLHWBiqgl+LNyr5YpIj2B1cBWXI9lArwANAEwxkx2/1CYAAzE9VjmPcaYDd761tUyA9Oej5/l3/f0sjqMKmHT3qO8tmo7gx+/CZu9dCOwnlaC3Pndbo6tSqbTs63yjyX/msqhj08wafHbfrN6pL/EEYgutlqmL57SWYPnMfqCbQzwSHmvpVR107lVA5632/jnG3MY8uQI7A57ic/1VMQMqRdE9rmcQsdqtoog/ezhYs+xoojpL3FUNTrTVik/1755ff7WvzPzx88mOyu7xOd5KkimH8/EEVb4h0bK3jRC3HsY+EsR01/iqGp0LR2lAkDbpnV5eXBX/vL6bG58eiQOp+uf7ldTvmHp1//lfOp5QiNDadSoIUeOHCX9bDp2u4OwhBDa3dkyfzw+acVZzh/PYPP/7SX7XA6OMDuZSVkM/uMNQMmLmF9N+YZlc5eTfjadkPAQ2nduR2paarl2ryrYJjg4mBMzE2kzqulF4wi03aispglfqQDRqlEMrw7rwXOvzWLwn25mwfTFxC2Mo9mY+kQ0Deb0nnMcnH2Q6B416XhDc1L2prHng3h2f+QaBolpEE2fvr1Z8d+V1OkVnl+0TVpxlhbtmgMlK2J+NeUb4hbG0fyOWGq2iuD0njQ2fbaJmEtq0+3FCwusJSnAemqzc/oBDs8+we6znuMoS2G3utOEr3zudOp5q0Oospo3qMNrN1/N06/NZumqH2l+VywRzUMIskNo3SCa316fI4uSsDmEqEsjaX1vo/yCLLiKoe3ubPl7MfQySG5yptDMUm8TopbNXU7zO2KJujQSgMgWobS4LZb9HyV4nK3rbQYseJ4l2/bu5iQvO8/LH/2vxzhK0q8qTMfwlc/ZW/Vk1S8HrA6jympcL4o3b72WtJNnCY0Nxi5gEzA5hhotwshM/n0mrasg+/ssWl+sGJl+1rU6Zh5jcqnRMoys878Xg0u7xWFZ4tLVL0tPE77yudpNLiW5QJJRvtcgpia1okLY/cFhyHAlWnEIZ/adIyiqwKzZAgVZ8E0xNCTcNTs3j4iNM/vO4Qz9vRhc2i0OdZZs5dCEr5SfWLx2BwOef5c297zMgOffZfHaHRdt361JIzJOZLLjvSNknMkm83gmBz47Ro2WoeRmG5J/TeXAzASuHXgtbz02ntTTaT5ZpbLf8Os5MDOB5F9Tyc02pO4/z/7PEohpX9tjnyW5ZlniqogVN6s6HcNXyg8sXruDZ2bOp8WwevRsVpekg2k8M3M+AIOuLLrauIvTBjXOCaf2n+eH/7eboHAHtgxIXHma4ytOExIewoDhAwh12kk6epA1X61g0L1DgPLNLB3x4DAAln28nPSzhwkJD6Fz586kpqV6XB2zJIVgnSVbOco907Yi6UzbwHTw1y10P7OUYVe39d5YATDg+XcJ6R9GTIGZpSf2nSF96TniXnnY6/kvfLaCqD90ovGlTQodP5OcytSH/8XEIeE8suAsD076C5G1IorpRVUFF5tpq0M6SvmBA8dOUadIAbJOswgOHDtVovNfHtWLo4vXc3DbwULHv/96JUNb2WhdL5ihrWys+WqFjyJWgUgTvlJ+oHn92iQVKUAmHUyjef3aJTrfZrMx/p6+JH23if2/7ANcd/fbl33P6CtcP0hGXxHB9mXfk3o67WJdqSpME75SfuDJYX3Y/81xju1JYc+hRI7tSWH/N8d5clifC9qePJ3Gzc9NJinlbKHjIsK/77iO1NVb2bNxT/7dfZ0IV6muToQj/y7/THJqfiG3Mmxes4VXH3+Np0c+x6uPv1ZltxD0d1q0VcoP5BVm/zT1K44kJtOwbhTjx47wWLCdsfAHko8d5qMF3/On2ws/kSIi/GvMH/jbzFWsW7GBdekZfL71eKE2NU5sB8BWpJBbUXRGrP/QhK98LiQsgp3bkxlmdSABptulTYh1CHPHNuKhBefo3rbpBW1Onk5jwcr1TBoRzUML1nPXkGuoUzO8UBsR4R+jexNkt5Hdrhltr25X6PP8Qu6Iujyy4Ht6juhToYVcnRHrP3RIR/lc/SYt2JYWSUqaLrFQGjMW/sCQVjYuqRvMkFY2PlrwfZna5PnrLdcSuusw21ZtLXS8sgu5OiPWf2jCVxUirEYdsnNyvTdUwO937nd2cd2t39klnAUr1xcapy9Jm6KeG3E1UQcT+OXbTYA1hVydEes/fJLwReQDEUkUkW3FfN5HRFJEZLP762++uK5S/q64AmtReXfuttxMNu46jN1k5t/B5/Ux6asVDGnl+id784eHERGPd/m7Dh2n+fAX2HM4kcVrd7B07Ubef/kDXhj1V758YyZtIzN5cE4C3d/Yz4NzEmgbmVmhd/k6I9Z/+GoMfzquLQxnXKTNamNMxVaHlPIzFyuwFrRi426OJmbw7/8ew26DnNxzNKoXRYPjuwFIPnaYOfGJOCSXCT+cppYjk27vxFM7MpQGx3cX6vu5ibOp7TjPXX+fTmq4ocWwegwZ25mNX/3GmuXrCKrpoMmQutSJDSYxIYONC09QL+6nCive6oxY/+GThG+MWSUizXzRl1JVRUkKrHnmvf4oX/z3Z54ZP4NvRoUxbOY5nr93GL07t+aWZ95y93GOyf8zjnEvT2PSkDAeWnCOWf95slCfuw4dZ+uv+/jqlnB6zjzGNU+0y5+92/WPzTi4PpHIthG06ePe0/YSiGlcl+RlFVtv8bbksqoclTmGf5WI/CIii0WkXXGNRGSsiGwQkQ2r5n1eieEp5VulKbACPPH6Z4zp4KRTfTtjOjh55N+fXNDHsxNmXbTP5ybO5rb2DjrWdxLsgHMhmYU+tzmF4Jo2Dn+XkH9MC6jVR2Ul/I1AU2PM5cA7wNziGhpjphpjuhpjuvYaOrqSwlPKt0pbYP3ivz8TLNk80t21tPEj3Z0ESzYfzluV38fgS0LY+us+busU5rHPvLv7h7q7lkNuF2Pn5MEzpGf+vg9ucISTGrFhRIYIh/57FNACanVSKc/hG2POFHi9SETeFZFoY4zeVqiAcfJ0Gg+++glTn7+j2KGZPHl35tHuWa7REY78O/KC4+27Dh1n4BNvcfZ8Og90ctIg0rWmfINI113+e5tSgbrc/OFhOjUM4bb2DrLTz7Il8SxtmtRjSCsb787+js174knPyOS29g5iI1x9PHtFEPcvS2JnUBCXd29M0sE0gtPtpHybSuNbawEZbP9kL5nHcy7YK7a0dG/ZwFApCV9E6gPHjTFGRLrj+s0iqTKuraxhCw7l0PHTXhNjIClpARZ+L8J+tjWx0PHiCqzJWTm8v0l4f1NWofYZ2YbuE45Qy5HJyv3nCXYI035OxCYGhyOdmKhIss1Gajsy2HEsnc2Sy/ubTuefn55t2P1xPKlLztK8fm0mPfhHAN78ZgXxx04RHhRMq3ZtypWcdSZt4PBJwheRz4E+QLSIxAMvAk4AY8xkYCTwkIhkA+eBUcaf12VW5dap/yjGT3mWT9o0tDoUnyhNARZcRVhvChZYR3x5jsUTn6N147oXXPeWZ97KL9L+6/HbGPPCO3x1SxgjvjzHxOfu5vm3PmXSkGiPRdziFFyyYcH63cz7aCnX3VW2xyR1Jm3g8MkYvjFmtDEm1hjjNMY0Msa8b4yZ7E72GGMmGGPaGWMuN8ZcaYz5wRfXVf7L7nAQVqOW1WH4TGkLsCVRsMB6W3sHz7wzy+t1H/q/jwudM+7VGeWOa0i3NoxsEsOy95dQlvswnUkbOHSmrVJelGWGqzdFC6wPdXcVZPcc/n0IqOh1b2kfQnJSErd2CHK/DyI5KYlbOoSUO67+XVpyxyWxLJ26qNRJX2fSBg5N+KpaKukMWCi+APvSe/Op3e8p1u04CBSe4Zqn6LG894/953Nua+/AKcLNM88QZBNua+/gqfFf5MeVd92aITb2xp/g/NkUbu/oJG63a5x/6Z4sbu/oJP3smUJxlfW3jz4dmnNfhyYsmTS/VElfZ9IGDt3iUFWY9R//g6n3dLE6DI/Gf7qUBctWMqRfb68F2KFPT+Bo4oXDE/EnUmkQnoMJq82mj//GTc9M5Lf9e2nSohVf//sRgAuO5b0/eNoQ4hQys3NpGCkcSTUEOWzkGBuX1Q9hSL/e7sLvSc6cTef8+XSyclz/HLJyIcRpIz0rF6fNtTpmw7q18uNqUDe6RDWE4qz99TAT1+1h0CNDsdlKdk+oT+n4j4ttcajLI6tqxxcF2LVbDzDq2Tf5YFgYw2cmMWv5xgIFWNfQTG6uKXQsbu3OQkXaT1953F1wDXPPon2gwCza9cz6z5MYY9xF23qlKsqWx5WXNsZht/PG23MZ/PjwEiV9nUkbGHRIR1U7vijAPvTvj7m9o5NO9R3c3tHJY699ekEBtmhRdtyrH1204OppFm1FFItLomvrBvz52stY/cWKSrmeqhya8FW14osC7NqtB0hOSuKRbu7i6WWuWbH3XxEMuAqwW3buY/OOvflF2VvaBZGbeZ57u7jajO0aTHJSEgPbuN6PvjyMrb/uY8ilvxdgv1r+E998t86nxeLS6NQyltN7jnAmObVSrqcqniZ8Va1cbAasN3mF3rGvfMTtHZ0E2YWbvzzL59uyGNPBic3kABAbYWdoaxttakN0mI29SZks3J3JmA5OsrNdewQ4BG7v6OSjn05y84eHST5zltvaO1iwIy0/rhhnOr0bZF4Q68RZ35W44FweIsLU+wewcuI8UpLOeD9B+T0t2qoK88PHr/L3GxrRuF6U1aHkK64AW5JCZ16hd/PhNILskJVjaFzTxqHTuQQ7BAM47K57qOycXLJyDMEOGzYxnM8yBNl/b5Pj3hwmM8fQLMrOkVSDwybkYqNhdCQAR06m4rRD3ajIQnFk5wq1nZklKjj7wtnzGTw4LY5rxg0hKqZWhV9Plc/Firaa8FWFycrMYOcnf+Wdsb2tDqXcis54LVxg9VxMLXpO0TbePi9JHJVRxAU4l57JuGlL6HH/DdSpX7vCr6fK7mIJX4d0VIVxBgXjdDqtDsMnSrtMsadzirYpS0HWqiJuWEgQU8cOYt37izlx5ESlXFP5niZ8pbwoWuj1tkyxp3OKtilL8bgiZvyWRkiwk2kPDmLTR8s4/lui9xOU39GEr/xOaWbBVkYceXvJ5s14nbf9DLe1d0CWa5coT4Vfb8XhshSPy1Nw9pUgp4MpDw5i66fLSThwrNKuq3xDJ14pv1OaZYgrI468vWQnr03h/Pl00nOEIDtM33KCulHp+e0LLn3sbXnkki6fXFBZzqkIToedyWMH8uj7S8kd0ZOGrarGiqjVgSZ85VdKOwu2cuIouJdsyWa8envipyxLH5RnuQRfczjsTLx/AI+/vxQz7CoatWlsdUiqBHRIR/kVq4qS3uIoSZG2urHbbbxzf39+m7+W33b+ZnU4qgQ04Su/YXVRsrg4PM2CtSIuf2Sz2Xjz3n4ci1vPwa0HrA5HeeGThC8iH4hIoohsK+ZzEZG3RWSviGwREf9cQlH53ImUc2Rn55SobVmLkp6WJS5tm4KF4qJxSPb5C2bB5u0lW7C47C/F5spms9l4/e6+nFqxiX2b91kdjroIn0y8EpFeQBowwxjT3sPnNwCPATcAPYC3jDE9vPWrE68C32+7ttD0t3ncP6iz17ZlnQXraVni0rYpuFxy3rLEeRKTU8nJyS00CxYg29io7cjIn/FamiWXqyJjDP/z2UpCelxK6yvaWB1OtVXhyyMbY1aJSLOLNBmG64eBAdaKSC0RiTXGJPji+sp/1Yiuz/m9JbvDL0tRsvC+sK5liYvuC+utTdFCcelmvLrOGXJtJ78oNltJRHj5tt787xer+TU7h0t7tLU6JFVEZY3hNwQOF3gf7z52AREZKyIbRGTDqnmfV0pwKnCVZF9Yb218MeNVi7ouIsJLo3rh3HaAHd97HOFVFqqshO/pVwyPwzXGmKnGmK7GmK69ho6u4LBUICvJvrDe2vhixmtJZt5WN38Z2ZPwPfFsXbnF6lBUAZWV8OOBgg/qNgKOVtK1VRWVd+ceG2EHXMsSF72D99bGFzNeF+5M8zrztjp69qarif7tOL98u8nqUJRbZU28mgc8KiIzcRVtU3T8XpXXpl2HWZeZxfubThc67gw6XOI2vpjxeuRkKjZyLzrztrp6amgPJixcz6alG+jcv6vV4VR7vnpK53OgDxANHAdeBJwAxpjJIiLABGAgcA64xxizwVu/+pRO4DudlEjI2kk8Nkz/sVdnk+M2sjcijK43dLc6lCqvMp7Suehgu/vpHM/PyymlqrxxA7rwwX838dM3P9Jj2FVWh1Nt6UxbpVSluLdvZzrn5vDjV2usDqXa0oSvKlRwSChbf0siNzfX6lCUH7jzuo5c6bTx/ayVVodSLWnCVxUqNDwSe8uebNe105Xb6F7tkUPHyc7KtjqUakcTvqpwQaHh+PPeyaryPTqoK/PHz9GkX8k04SulKl2bRtH8a0g35r8+m6zMLKvDqTY04SulLNGyUTT/Hn4lC16bRWZGptXhVAua8JVSlmkaW5vX/3gNC16bRcb5DKvDqfI04SulLNWobhRvjerFotdnk34u3fsJqsw04SulLBcbXZN3xvRh8euzOZd23upwqixN+Eopv1A3KpJ377qepW/M4eyZ6rvSaEXShK+U8ht1aoYz6e6+LHvra9JS0qwOp8qprNUyVRm88uho0tJSLzgeERHJ8xMCZ3OY2g1bMvvH1XRs5XHPG6UKiaoRxpR7+zHu7bn84ZGh1Khdw+qQqgxN+H4sLS2VFve/c8Hx/e89ZkE0ZdegxaWsXhnpvaFSbjUjQpl6X3/GTZzPtQ8NoVZ0TatDqhJ0SEdVCptd/6qp0okMD2HqA/35fvICTiUmWx1OlaD/CpVSfis8NJipYwewdupCTiYkWR1OwPNJwheRgSKyS0T2ishzHj7vIyIpIrLZ/fU3X1xXKVX1hQYHMXXsIH7+II4TR05YHU5AK/cYvojYgYlAP1x7164XkXnGmB1Fmq42xgwp7/Wqu2OH95N8MpG/3F34P2WgFXKVKo2QYCdTHhzIQ9Pi6HD7ddRvUs/qkAKSL4q23YG9xpj9AO59a4cBRRO+KqWIiMgLCrTJJxMJiW5Ei/tfL3Q80Aq5SpVWkNPB5LEDeXhaHOaW3sS2iLU6pIDji4TfEDhc4H08ro3Ki7pKRH4BjgJ/NsZs98G1qzRPd+x/uXvIBcleqerC6bAz6YEBPPp+HLkjrqWhPupbKr4Yw/e0YW7Rxc83Ak2NMZcD7wBzi+1MZKyIbBCRDavm6RCFUqowR1gKE/+RyfE1/6BN1v3c2PppLq/3JWFOLep644uEHw80LvC+Ea67+HzGmDPGmDT360WAU0SiPXVmjJlqjOlqjOnaa+hF90ZXASQsuhHLNx+wOgwV6Grshk6vYG/yLa/+XzpzZmWza1sSbaMXMajlC9QN15Hki/HFkM56oLWINAeOAKOA2wo2EJH6wHFjjBGR7rh+0FS7H8feZs4+NKATxm7//QNjAIHcbOrEun6mnko8xpmJjxIz+IlCfaQknSzRNazSadAYvvzgL1zfqbllMagAF3QKLp0GjgyYD7ZX4OVf4MWPIPsp6P50Btc2fovF+/7Fuaw6Vkfrl8qd8I0x2SLyKBAH2IEPjDHbRWSc+/PJwEjgIRHJBs4Do0w13PPO28xZY7fT+NFP8o9nnvyNoOgmHP3g0fzzHHt3kDjrJZIWjC/Uh8nNLtE1rCIiOIOclsagAlzs6vxkzzDAuMaTXzoH//gzZGXDNc9m0CpqOVsSb7E4WP/kk6UV3MM0i4ocm1zg9QRggi+uVd3ZHU6CImvT8dFJhY5bndCVqnDRG13fX6FQlVCAvwKvvAvZV0LXq37ShF8MnWmrlAoMDveSyVsu/EiA55Ng3jwIdlw4pKlcdPG0SpSUcJhTr9ya/z43KwOxOwDDuBuuAANHpz+BLSiUun/8OwAmN7dQHznZWWSmnmLLhIcKHc9OPVnh8StlqexwsGdCR+DHCz+Wy6F/f3hjvIPGgyo9uoCgCb8y2R00euSj/LdHpz9Bg7vfIjPxAEF1m5N5fD9B9VqQMP1JbM4gAMRW9JcwwR4RRYO73yx09NCEOys4eKUsdrILNFwOz5M/hp9PgOdhwAAguS2zp8dx/d0DLAnTn2nCr0SCYLIzCx0rWLs2GDITD5CdepL4iXfm392bnOz8MfpTicdw1KxHxsnfCvVjE9cPBk+zc/OOKxXQEq6Femvgxgz4BngV1/BOR1w/BIYA2cEMaHUj9lOn+fy9xfS9byAinqYKVU+a8CuR2Gw4g4ILHyvwl1HsToKim2APr0WXJ9/LP77/vcf45/QFQN5M2wufwsmo45rWoOvpqCorszb8+oDr0cwbM+DGIp9nB7s+z6xN3061cdptTJ+6kP5jB2vSd9OirVIqcJxpA5ufh/i+kBEFOUGu7/F9XcfPtMlv2rtDM+7v2Iwlk+ZTDZ8C90j8+T/EtFX7/TY4bxOcHh/ag+zcwuHnZGbgqPX7Kn/Zp49hc/5+x19wCCevmAtS4L27XU4WIbUbFOo7O/UkExdu8NuJVwBrZ77BQ90j6dpGF71SleenXfFMWLuLQY8Ow3ZBTazqGdXurmJ/ndEhnTLyNsEpO9fQ9NEZhT478NZtRN/wZP7741/8lQZjp+W/z045jrN2IxKmP07s3W+TdSoeZ53GJHz4GA3udU1jMMYQP+EO6gz5U6G+E7/4W4nislKPW5/ki4+f1YSvKlWPSxrhtAmvv/U1gx+/qVrvvqYJv1IJzuim+U/eiM2GzRlMblZG/p1+wc+AYsceGzZrXeh93hi+PxMRdChVWaFL64Y8a7fz6ptzGPzECOwOu/eTqqDq+6NOKVWtdGxRn7/268z8N+aQnZVtdTiW0ISvlKo22jatyz8GXcGC8dUz6WvC95Fjh/dz5OCe/O0Hc3NzyMrMIDsz46Ln5RXNi37PzXKdV3SmrVKqfFo3juFfN3Zn/muzyMrMsjqcSqVj+GVUdIJT8slEnBG187cfPPXKLRyZ8gDG5GCzucYLTU4W8RN/nxFrcrKIn3BHgV5/fyrn6NQHCj21c/idMYXOK1qEzZtYpROvlPKuRcM6/GfEVfz5P7MY8vRIgkKCrA6pUuhjmT5S3ISogpOmvJ2z/p8jafzYJ5jc3EJLKhx+ZwyTF//s+6AtsOfjZ/j3Pb2tDkMpAI6cOM1TM1dzw59GEhIW7P2EAHCxxzJ1SEcpVW01jKnF27f1ZtHrszh/9rzV4VQ4TfiqUvnxL5SqmqpfpwYT7/gDS8bP4Vxa1U76Pkn4IjJQRHaJyF4Rec7D5yIib7s/3yIiXXxxXRV4jqSH8NuxU1aHoVQhMVGRvHvX9cSNn8PZM2etDqfClLtoKyJ2YCLQD9eG5utFZJ4xpuBuwoOA1u6vHsAk9/cqoyzF0qLnmJysQsXZfDlV50mCpj1HsOXAcprUr211KEoVUqdmOFPu7ctDb33NdY8NJ7JWhNUh+ZwvntLpDuw1xuwHEJGZuFarLpjwhwEz3PvYrhWRWiISa4xJ8MH1/UJZ1qmxem0bpVRhtSLDmHJfP8a9M5c+jwylRu0aVofkU74Y0mkIHC7wPt59rLRtABCRsSKyQUQ2rJqnCVEpVblqhIcy9f4BrJw4n9MnT1sdjk/5IuF7egSoaGmuJG1cB42Zaozpaozp2mvo6HIHp5RSpRURFsy0sQP4YfJCTh1Ptjocn/FFwo8HGhd43wg4WoY2SinlN8JCgpgydgA/vbeIkwlJVofjE75I+OuB1iLSXESCgFHAvCJt5gF3up/WuRJIqUrj90qpqik0OIipYwfy84dxnEoM/Dv9cid8Y0w28CgQB+wEvjTGbBeRcSIyzt1sEbAf2AtMAx4u73WVUqoyBAc5eWpAZ7at3GJ1KOXmk7V0jDGLcCX1gscmF3htgEd8cS2llKpsHVs1pPm2w/zy3WYu/0Mnq8MpM51pqypVTIMmzP7pEDk5ugqoCiz/b/iV1Dtygk3LAnddK034qlJF1qqNo/6lpJ5LtzoUpUrtyRt70ORkChuXrLc6lDLRhK8qXXHbNioVCB65oSutUs+ybsFaq0MpNU34SilVSmP7d6FDZhY/ffOD1aGUiiZ8pZQqg3uuv5wryOWH2autDqXENOErpVQZjenTkWtCHaz+YoXVoZSIJnyllCqHW3u24/qaoaz89FurQ/FKE75SSpXTiKvaMrhuDb6bsczqUC5KE75SSvnAkO5tGN6oDss/iMNf9wrXhK8skeun/yCUKo9BV7RidKt6LJu22C+TviZ8Vema9xjIy19usDoMpSrEdZe34J52jYibvMDvkr4mfFXpYho156y9+K0flQp017ZvxoOdW7Bk4jy/Svqa8JVSqgJc1bYxj/Zow8K355Kb6x9rR2nCV0qpCtKtTUP+fO1lLHzra3L9YMFATfhKKVWBOrWM5fk/dGD+G3PIyc6xNBZN+EopVcHaN6/PiwO6MH/8bLKzsi2Lo1wJX0Rqi8gyEdnj/h5VTLuDIrJVRDaLiD6eoZSqdi5tEsPLg7sy/3Xrkn557/CfA5YbY1oDy93vi/MHY0wnY0zXcl5TKaUCUqtGMbw6rAfz/vMlmRmZlX798ib8YcBH7tcfAcPL2Z9SSlVpzRvU4fWR17DgtdlknM+o1GuXN+HXM8YkALi/1y2mnQGWisjPIjL2Yh2KyFgR2SAiG1bN+7yc4Sl/lZWV7TePqilV2RrXi+LNW69l4euzK/XfgdeELyL/FZFtHr6GleI61xhjugCDgEdEpFdxDY0xU40xXY0xXXsNHV2KS6hA0qTnSF6ds87qMJSyTIOYmvRoHE3C/oRKu6bXhG+M6WuMae/h6xvguIjEAri/JxbTx1H390Tga6C77/4IKhA1bNOBk2nWPqKmlNWeGNKd3XNWc3Tf0Uq5XnmHdOYBd7lf3wV8U7SBiISLSGTea6A/sK2c11VKqYDncNh594GB7Jmzmvg98RV+vfIm/FeBfiKyB+jnfo+INBCRRe429YA1IvILsA5YaIxZUs7rKqVUlWC325hw/wAOzfuBw7/+VqHXcpTnZGNMEnC9h+NHgRvcr/cDl5fnOkopVZXZ7Tbeurc/T09fTk52Ls3aN6uQ6+hMW6WU8gM2m43x9/Ql6btN7P9lX8Vco0J6VUopVWoiwr/vuI60NdvYs3GPz/vXhK+UUn5ERPjn7X3IWvcru9b96tO+NeEry/jDcrFK+SMR4e+je2Pfsp+dP2z3Wb+a8JVlzke1ZuXWin0qQalA9j9/7EnorsNsW7XVJ/1pwleWaXn1YLYdPGF1GEr5tedGXE3UwQR++XZTufvShK+UUn7u6WFXEnvsFJuW/VyufjThK6VUAHh8cDeanUphw6Kyr0GlCV8ppQLEQwO70vbcedbNX1um8zXhK6VUALmvX2cuz85i7dffl/pcTfhKKRVg7rrucrrZ4fvZq0p1niZ8pZQKQLf37kCvMCerZn5X4nM04SulVID64zXt6F8rjJWfLi9R+3KtllnRoiODrA5BVSBHVhih9WIhvLidMZVS3gzvWxfH2q1sWbOPK/p2u2hbMcZUUlilJyJjjTFTrY7DG43T9wIlVo3T9wIl1kCJsyB/H9K56IbnfkTj9L1AiVXj9L1AiTVQ4szn7wlfKaWUj2jCV0qpasLfE36gjI9pnL4XKLFqnL4XKLEGSpz5/Lpoq5RSynf8/Q5fKaWUj2jCV0qpasIvE76IDBSRXSKyV0Seszqe4ojIByKSKCLbrI7lYkSksYh8JyI7RWS7iDxhdUyeiEiIiKwTkV/ccb5kdUwXIyJ2EdkkIgusjuViROSgiGwVkc0issHqeIojIrVEZLaI/Or+u3qV1TF5IiKXuP9b5n2dEZEnrY6rJPxuDF9E7MBuoB8QD6wHRhtjdlgamAci0gtIA2YYY9pbHU9xRCQWiDXGbBSRSOBnYLi//TcVEQHCjTFpIuIE1gBPGGPKthZsBRORPwFdgRrGmCFWx1McETkIdDXGnLQ6losRkY+A1caY90QkCAgzxpy2OKyLcuerI0APY8whq+Pxxh/v8LsDe40x+40xmcBMYJjFMXlkjFkFnLI6Dm+MMQnGmI3u16nATqChtVFdyLikud863V/+dUfiJiKNgMHAe1bHUhWISA2gF/A+gDEm09+Tvdv1wL5ASPbgnwm/IXC4wPt4/DA5BSoRaQZ0Bn6yOBSP3MMkm4FEYJkxxi/jBN4EngFyLY6jJAywVER+FhF/nR3aAjgBfOgeJntPRMKtDqoERgGfWx1ESfljwhcPx/zyLi/QiEgEMAd40hhzxup4PDHG5BhjOgGNgO4i4ndDZSIyBEg0xpRvg9HKc40xpgswCHjEPRTpbxxAF2CSMaYzcBbw2/odgHvYaSgwy+pYSsofE3480LjA+0bAUYtiqTLcY+JzgE+NMV9ZHY837l/nVwADrY3Eo2uAoe6x8ZnAdSLyibUhFc8Yc9T9PRH4Gtewqb+JB+IL/EY3G9cPAH82CNhojDludSAl5Y8Jfz3QWkSau3+CjgLmWRxTQHMXQ98HdhpjxlsdT3FEJEZEarlfhwJ9gV8tDcoDY8zzxphGxphmuP5+fmuMGWNxWB6JSLi7UI97iKQ/4HdPlRljjgGHReQS96HrAb96qMCD0QTQcA744Xr4xphsEXkUiAPswAfGmO0Wh+WRiHwO9AGiRSQeeNEY8761UXl0DXAHsNU9Pg7wgjFmkXUheRQLfOR+8sEGfGmM8etHHgNAPeBr1898HMBnxpgl1oZUrMeAT903evuBeyyOp1giEobrScIHrY6lNPzusUyllFIVwx+HdJRSSlUATfhKKVVNaMJXSqlqQhO+UkpVE5rwlVKqmtCEr5RS1YQmfKWUqib+P1ONH/f8BacFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in [0.4, 0.5, 1.0, 5.0, 100]:\n",
    "\n",
    "    counterfact = create_counterfactual(x_reference=X[15], \n",
    "                                        y_desired=2, \n",
    "                                        model=clf, \n",
    "                                        X_dataset=X,\n",
    "                                        y_desired_proba=1.0,\n",
    "                                        lammbda=i, \n",
    "                                        random_seed=123)\n",
    "\n",
    "\n",
    "    ax = plot_decision_regions(X, y, clf=clf, legend=2)\n",
    "    ax.scatter(*counterfact,\n",
    "               **scatter_highlight_defaults)\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the stronger the $\\lambda$ value, the more the first term in the loss\n",
    "\n",
    "$$L\\left(x, x^{\\prime}, y^{\\prime}, \\lambda\\right)=\\lambda \\cdot\\left(\\hat{f}\\left(x^{\\prime}\\right)-y^{\\prime}\\right)^{2}+d\\left(x, x^{\\prime}\\right).$$\n",
    "\n",
    "dominates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Applying Wachter et al.'s threshold concept,\n",
    "\n",
    ">4. Optionally, as the authors recommend, you can repeat steps 2 and 3 by increasing $\\lambda$ until a user-defined threshold $\\epsilon$ is reached, i.e.,\n",
    "    - while $\\left|\\hat{f}\\left(x^{\\prime}\\right)-y^{\\prime}\\right|>\\epsilon$:\n",
    "        - increase $\\lambda$\n",
    "        \n",
    "we can define a user-defined threshold and implement it as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial lambda: 0.0\n",
      "Initial diff: 0.9999998976132334\n",
      "Final lambda: 1.1\n",
      "Final diff: 0.2962621523225484\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "\n",
    "desired_class_2_proba = 1.0\n",
    "\n",
    "for i in np.arange(0, 10000, 0.1):\n",
    "\n",
    "    counterfact = create_counterfactual(x_reference=X[15], \n",
    "                                        y_desired=2, \n",
    "                                        model=clf, \n",
    "                                        X_dataset=X,\n",
    "                                        y_desired_proba=desired_class_2_proba,\n",
    "                                        lammbda=i, \n",
    "                                        random_seed=123)\n",
    "\n",
    "    predicted_class_2_proba = clf.predict_proba(counterfact.reshape(1, -1))[0][2]\n",
    "\n",
    "    if not i:\n",
    "        print('Initial lambda:', i)\n",
    "        print('Initial diff:', np.abs(predicted_class_2_proba - desired_class_2_proba))\n",
    "    \n",
    "    \n",
    "    if not np.abs(predicted_class_2_proba - desired_class_2_proba) > 0.3:\n",
    "        break\n",
    "    \n",
    "    \n",
    "ax = plot_decision_regions(X, y, clf=clf, legend=2)\n",
    "ax.scatter(*counterfact,\n",
    "           **scatter_highlight_defaults)\n",
    "\n",
    "print('Final lambda:', i)\n",
    "print('Final diff:', np.abs(predicted_class_2_proba - desired_class_2_proba))\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## API"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "## create_counterfactual\n",
      "\n",
      "*create_counterfactual(x_reference, y_desired, model, X_dataset, y_desired_proba=None, lammbda=0.1, random_seed=None)*\n",
      "\n",
      "Implementation of the counterfactual method by Wachter et al.\n",
      "\n",
      "References:\n",
      "\n",
      "- Wachter, S., Mittelstadt, B., & Russell, C. (2017).\n",
      "Counterfactual explanations without opening the black box:\n",
      "Automated decisions and the GDPR. Harv. JL & Tech., 31, 841.,\n",
      "https://arxiv.org/abs/1711.00399\n",
      "\n",
      "**Parameters**\n",
      "\n",
      "\n",
      "- `x_reference` : array-like, shape=[m_features]\n",
      "\n",
      "    The data instance (training example) to be explained.\n",
      "\n",
      "\n",
      "- `y_desired` : int\n",
      "\n",
      "    The desired class label for `x_reference`.\n",
      "\n",
      "\n",
      "- `model` : estimator\n",
      "\n",
      "    A (scikit-learn) estimator implementing `.predict()` and/or\n",
      "    `predict_proba()`.\n",
      "    - If `model` supports `predict_proba()`, then this is used by\n",
      "    default for the first loss term,\n",
      "    `(lambda * model.predict[_proba](x_counterfact) - y_desired[_proba])^2`\n",
      "    - Otherwise, method will fall back to `predict`.\n",
      "\n",
      "\n",
      "- `X_dataset` : array-like, shape=[n_examples, m_features]\n",
      "\n",
      "    A (training) dataset for picking the initial counterfactual\n",
      "    as initial value for starting the optimization procedure.\n",
      "\n",
      "\n",
      "- `y_desired_proba` : float (default: None)\n",
      "\n",
      "    A float within the range [0, 1] designating the desired\n",
      "    class probability for `y_desired`.\n",
      "    - If `y_desired_proba=None` (default), the first loss term\n",
      "    is `(lambda * model(x_counterfact) - y_desired)^2` where `y_desired`\n",
      "    is a class label\n",
      "    - If `y_desired_proba` is not None, the first loss term\n",
      "    is `(lambda * model(x_counterfact) - y_desired_proba)^2`\n",
      "\n",
      "\n",
      "- `lammbda` : Weighting parameter for the first loss term,\n",
      "\n",
      "    `(lambda * model(x_counterfact) - y_desired[_proba])^2`\n",
      "\n",
      "\n",
      "- `random_seed` : int (default=None)\n",
      "\n",
      "    If int, random_seed is the seed used by\n",
      "    the random number generator for selecting the inital counterfactual\n",
      "    from `X_dataset`.\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('../../api_modules/mlxtend.evaluate/create_counterfactual.md', 'r') as f:\n",
    "    s = f.read() \n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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